As the frequency of an ac circuit increases, the current first increases and then decreases. What combination of circuit elements is most likely to comprise the circuit ?

Options

A. Inductor and capacitor.
B. Resistor and inductor
C. Resistor and capacitor.
D. Resistor, inductor and capacitor.

Answer

A, D

Explanation

Reactance of an inductor of inductance
`X_L=2pivL " " therefore X_L prop v`
where v is frequency of the AC circuit,
reactance of the capacitor `X_C=1/(2pivC)`
`therefore X_C prop 1/v`
On increasing frequency v clearly `X_L` increases and `X_C` decreases.
For L-C-R circuit
`Z=sqrt(R^2+(X_L-X_C)^2)`
where Z=impedence of the circuit
`=sqrt(R^2+(2pivL-1/(2pivC)^2)`
As frequency (v) increases, Z decreases and a certain value of the frequency known as resonant frequency `v_0` impedence Z is minimum that is `Z_"min" = R`, current varies inversely with impedence and at `Z_"min"` current is maximum.